First, buy the club. Then interact with Lilly & ask her about the club & dating.
Then while there, call a dateable girl (Gwen Madison Veronica Jessica are "dateable". ). They will mention what alchohol they want to drink. Talk to Lilly & buy that in the main bar, then call again confirm the date.
They will ask three questions about how much you've paid attention to their life & backstory. If you answer all questions correctly you get optional h-scene, & progress Trickster storyline.
Hint: Gwen is the cheapest & easiest girl to fully date, if you're struggling with the others